{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"../assets/logo.png\" width=\"50\" align=\"left\"> \n",
    "\n",
    "# Angle of Arrival\n",
    "\n",
    "***\n",
    "\n",
    "#### Prerequesites\n",
    "- Sampling Data\n",
    "- Range\n",
    "- Doppler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Intro - How Can We do Better?\n",
    "\n",
    "<img src=\"../assets/protractor.png\" width=\"400\">\n",
    "\n",
    "Unfortunately with the current hardware we have been experimenting with, we are already quickly approaching a ceiling. We have already extracted the two key pieces of information range and doppler from our radar. You may start thinking there couldn't possibly be anything else we can do. However, let's theory craft for a little bit and revisit why we could even gather this information in the first place. We were able to obtain range from understanding that our transmitted EM waves would bounce off a target. Sampling *multiple* points of this return would allow us to quantize what's at different ranges relative to the radar. Doppler was similar in that the only thing we added to our logic was sending out *multiple* chirps. Each of these chrips captured snapshots with close proximity in time such that the radar's receiver could \"see\" micromovements of objects and translated them into velocity readings. So, now I ask **you** what can we now do better?\n",
    "\n",
    "Well, to lead you in the right direction, it will probably have something to do with *multiple* of something based on my forced hints in the previous paragraph. If you still need help thinking of something, what if I told you that you shouldn't limit yourself to the current hardware...\n",
    "\n",
    "Ha! I bet some of you just thought of glueing multiple radars together which just sounds preposterous. Still, that kind of thinking is exactly what we need to move forward. Let's just tune it so that it ends up slightly more feasible than before."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What is MIMO?\n",
    "\n",
    "We have breifly mentioned before that the radar we have been using (or assumed we were using) has only **1 TX** and **1 RX**, or 1 transmitter and 1 receiver. This is not always the case even in some of the past exercises we have done. Humoring the thought of physically glueing together our radar to a copy of itself we can do simple math and say our radar now has (1+1) TX and (1+1) RX. Great! What does it mean though, we must get double the range resolution? No...we already proved in the range module that range resolution is a function of the signal bandwidth. To really understand what we just did and the value of it, let's learn about something called MIMO first.\n",
    "\n",
    "MIMO is short for Multiple Input - Multiple Output and is exactly what it sounds like. In fact, by glueing together our radars we technically would have made a MIMO radar. In this kind of model, we can now utilize the fact that we have 2 TX (Multiple Outputs) that sends out two different EM waves and each of them would be received by 2 RX (Multiple Inputs). But wait, previously each of our TX would map to a single RX so doesn't this mess everything up and give us redundant data? Actually, this is a good thing and we aren't just taking a signal and naively duplicating it. In fact, we are capturing a new \"perspective\" of the same signal with each RX and this is important. Let's say one of our TX's sent a signal that hit an object and it was about to be received by both of our RX shortly after. Stop. We need to be very careful about how we describe the next few steps in the process."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Angle of Arrival \n",
    "\n",
    "If we were to describe this without thinking, we could say \"and then both RX's received the signal,\" which hides the point I'm trying to make. In what order did the RX receive the signal (RX 1 $\\rightarrow$ RX 2 or vice versa)? How long did it take the latter to receive it? This all matters. Truth be told, we really didn't need to talk about MIMO right at this moment complete this module, but they relate in a nice way and you will see why shortly. Think about the information we get from knowing which was first and by how long. Try drawing out this event, namely draw the TX we used, the 2 RX, an object, and the signal between everything. Remember that even though the signal is traveling fast, it still must travel at a constant speed of $c$. Figure out what you can tell from knowing that one or the other RX received the signal first. What about the case when they receive the signal at the same time? Maybe your drawing looks something like this...\n",
    "\n",
    "<img src=\"../assets/simple_aoa.png\" width=\"600\">\n",
    "\n",
    "Anything to the left of the radar follows the rule that it gets receieved by RX 1 first then RX 2. This is reversed for any object on the right side of the radar. By now, I think you should be able to connect the dots and see that by \"glueing\" radars together we can obtain the angle of which a wave arrives. Namely, we can now **pinpoint where an object is in a new dimension**. In radar terminology, this new dimension/measurement is called **azimuth**, a fancy term for angle. We can finally put what you are seeing in the picture into words. Any object in front of the radar will force a signal to return and hit the receivers in a specific order. The timing is dependent on first the angle of the object relative to the radar (call this $\\theta$), and then the distance between each RX (call this $l$). If we assume that the incoming signal is made up of roughly parallel rays, the math becomes clear and the extra path length $\\Delta d$ simplifies to $l \\cdot sin(\\theta)$. Although this may be hard to solve directly, we can once again rely on the phases of the waves at each RX to provide more information. It turns out that the exact phase difference between the two respective signals at each RX is proportional to this $\\Delta d$ term. Using a FFT will extract the approximate angle of arrival of our signal.\n",
    "\n",
    "In code, we will go over how to take the FFT to measure azimuth..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Processing Azimuth Information\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 1 - Range FFT\n",
    "\n",
    "Again, let's get our range information so we get some reference of what we're looking at. We've already done this a few times, so I won't bore you. What you may want to keep in mind is that we have inserted a new dimension into our data, so there are some slight changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of frame: (128, 8, 128)\n"
     ]
    }
   ],
   "source": [
    "# Read in frame data\n",
    "frame = np.load('../assets/doppler_example_1.npy')\n",
    "\n",
    "# Manually cast to signed ints\n",
    "frame.real = frame.real.astype(np.int16)\n",
    "frame.imag = frame.imag.astype(np.int16)\n",
    "\n",
    "print(f'Shape of frame: {frame.shape}')\n",
    "\n",
    "# Meta data about the data\n",
    "num_chirps = 128 # Number of chirps in the frame\n",
    "num_samples = 128 # Number of ADC samples per chirp\n",
    "\n",
    "num_tx = 2\n",
    "num_rx = 4\n",
    "num_vx = num_tx * num_rx # Number of virtual antennas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "range_plot = np.fft.fft(frame, axis=2)\n",
    "\n",
    "# Visualize Results\n",
    "plt.imshow(np.abs(range_plot.sum(1)).T)\n",
    "plt.ylabel('Range Bins')\n",
    "plt.title('Interpreting a Single Frame - Range')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2 - Doppler FFT\n",
    "\n",
    "We can also use the knowledge we obtained from the last module and extract doppler information from the radar data. You should know how to do this one already also."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "range_doppler = np.fft.fft(range_plot, axis=0)\n",
    "range_doppler = np.fft.fftshift(range_doppler, axes=0)\n",
    "\n",
    "# Visualize Results\n",
    "plt.imshow(np.log(np.abs(range_doppler).T).sum(1))\n",
    "plt.xlabel('Doppler Bins')\n",
    "plt.ylabel('Range Bins')\n",
    "plt.title('Interpreting a Single Frame - Doppler')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3 - Azimuth FFT\n",
    "\n",
    "Now for the new stuff. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#################### TODO ####################\n",
    "\"\"\"\n",
    "    Task: Perform the range FFt on the entire frame\n",
    "    Output: range_azimuth [azimuth_bins, range_bins]\n",
    "    \n",
    "    Details: There are three basic things you will need to do here:\n",
    "                1. Zero pad each virtual antenna array (axis 1) from 8 elements to num_angle_bins elements\n",
    "                2. Perform the Azimuth FFT\n",
    "                3. Accumlate result over all doppler bins (for visualization purposes)\n",
    "\"\"\"\n",
    "num_angle_bins = 64\n",
    "\n",
    "# Zero pad input\n",
    "\n",
    "# Azimuth FFT\n",
    "\n",
    "# Accumulate over all doppler bins\n",
    "\n",
    "##############################################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\" REMOVE \"\"\"\n",
    "padding = ((0,0), (0,num_angle_bins-range_doppler.shape[1]), (0,0))\n",
    "range_azimuth = np.pad(range_doppler, padding, mode='constant')\n",
    "range_azimuth = np.fft.fft(range_azimuth, axis=1)\n",
    "range_azimuth = range_azimuth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize Results\n",
    "plt.imshow(np.log(np.abs(range_azimuth).sum(0).T))\n",
    "plt.xlabel('Azimuth (Angle) Bins')\n",
    "plt.ylabel('Range Bins')\n",
    "plt.title('Interpreting a Single Frame - Azimuth')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Extras\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivation for Other Uses\n",
    "\n",
    "When I first learned about AOA, it was completely foreign and seemed like a specific piece of knowledge that could only be applied to the radar space. Not necessarily true. The math might change slightly, but the concepts undeniably can transfer. There are two examples off the top of my head: WiFi and smart home devices. For smart home devices, I'm talking about devices like Amazon's Alexa. If you have ever used one, you know that you need to signal the device using the phrase \"hey Alexa\" and it starts listening. Moreover, if you have ever looked that the device while saying that, you may have noticed that the many LED's converge in a way that points directly at you. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Recap\n",
    "\n",
    "This module completes our studies of what useful information radar offers. In addition to range and doppler, we now know the basics of how we can use radar to gain **Angle of Arrival**. In short, the backscatter of an object can be analyzed to find the slight difference in time of arrival to one RX compared to another. However, we also learned that this means it is impossible to obtain  this information without **at least 2 RX**. In contrast, we gain **additional angular resolution by adding more RX (and virtual antennas)**. Since it gets physically harder to add more and more RX, we can resort to adding **additional TX as well as RX**. This creates a special model called a **Multiple Input Multiple Output** array, simulating **virtual antennas** that take the place of our RX. For example, with 2 TX and 4 RX, we have 8 virtual antennas. By adding one more TX, we now get 12 virtual antennas allowing us to get even more resolution."
   ]
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    "## Looking Forward\n",
    "\n",
    "After completing all the basics modules, you have learned how to begin utilizing a radar in the real world. You could quit now...or you could start learning about more advanced techniques. Somewhere along the line you may have noticed that I haven't really showed you how to do anything useful with the data we extracted. It also may seem like everything is washed down. It is. What lies ahead is exciting and will talk about new topics like **noise** and **noise removal** while we're at it, even advanced mathematical ways to improve on this AOA module called **beamforming**, and many more (dare I say **ML/DL**). I encourage you to look into more. This way you can learn how to make your very own pipeline to hopefully accomplish some substantial task and solve some real-world problem. I assure you that all these things are more involved than just taking another FFT."
   ]
  },
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   "source": [
    "***\n",
    "\n",
    "#### Contributors\n",
    "- Dash Kosaka\n",
    "\n",
    "#### Questions, Issues, etc.?\n",
    "Contact by...\n",
    "- email - presenseradar@gmail.com\n",
    "- github - https://github.com/presenseradar/openradar"
   ]
  }
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